Chiral perturbation theory at O(a^2) for lattice QCD

TL;DR

This paper develops the chiral effective Lagrangian at order a^2 for lattice QCD with Wilson and Ginsparg-Wilson fermions, including new terms and corrections, and computes light meson masses with these effects.

Contribution

It constructs the chiral Lagrangian at order a^2 for specific lattice theories, including new terms and corrections, and analyzes meson mass corrections at this order.

Findings

Few new terms appear at order a^2 in the Lagrangian.

Corrections to continuum coefficients are proportional to a^2 and appear at higher orders.

No order a^2 corrections to valence-valence meson mass at next-to-leading order.

Abstract

We construct the chiral effective Lagrangian for two lattice theories: one with Wilson fermions and the other with Wilson sea fermions and Ginsparg-Wilson valence fermions. For each of these theories we construct the Symanzik action through order $a^2$. The chiral Lagrangian is then derived, including terms of order $a^2$, which have not been calculated before. We find that there are only few new terms at this order. Corrections to existing coefficients in the continuum chiral Lagrangian are proportional to $a^2$, and appear in the Lagrangian at order $a^2 p^2$ or higher. Similarly, O(4) symmetry breaking terms enter the Symanzik action at order $a^2$, but contribute to the chiral Lagrangian at order $a^2 p^4$ or higher. We calculate the light meson masses in chiral perturbation theory for both lattice theories. At next-to-leading order, we find that there are no order $a^2$ corrections to the valence-valence meson mass in the mixed theory due to the enhanced chiral symmetry of the valence sector.